Complexity of Bezout ’ S Theorem Iv : Probability of Success ; Extensions

@inproceedings{Shub1996ComplexityOB,
title={Complexity of Bezout ’ S Theorem Iv : Probability of Success ; Extensions},
author={Michael Shub and Steve Smale},
year={1996}
}

Michael Shub and Steve Smale Abstra t. We estimate the probability that a given number of projective Newton steps applied to a linear homotopy of a system of n homogeneous polynomial equations in n + 1 complex variables of fixed degrees will find all the roots of the system. We also extend the framework of our analysis to cover the classical implicit function theorem and revisit the condition number in this context. Further complexity theory is developed.

Sphere Packings, Lattices and Groups, Springer, New York, 1988. Demmel, J., On condition numbers and the distance to the nearest ill-posed problem, Numerische Math

J. 1–46. Conway, N. Sloane

1988

On condition numbers and the distance to the nearest illposed problem